# Anticanonical codes from del Pezzo surfaces with Picard rank one

## TL;DR

This paper constructs algebraic geometric codes from del Pezzo surfaces with Picard rank one, focusing on anticanonical classes, and demonstrates some codes outperform existing best known codes.

## Contribution

It provides explicit constructions of del Pezzo surfaces of degrees 4, 5, and 6 and analyzes the parameters and automorphisms of the associated anticanonical codes.

## Key findings

- Codes with excellent parameters were obtained.
- Some codes outperform the best known codes in the database.
- Automorphisms of surfaces relate to code isomorphisms.

## Abstract

We construct algebraic geometric codes from del Pezzo surfaces and focus on the ones having Picard rank one and the codes associated to the anticanonical class. We give explicit constructions of del Pezzo surfaces of degree 4, 5 and 6, compute the parameters of the associated anticanonical codes and study their isomorphisms arising from the automorphisms of the surface. We obtain codes with excellent parameters and some of them turn out to beat the best known codes listed on the database codetable.